If A= [ array ccc 1 & 2 & 3 -1 & 1 & 2 1 & 2 & 4 array ] and A_ i j is a cofactor of a_ i j , then the value of a₂₁ A₂₁+a₂₂ A₂₂+a₂₃ A₂₃ is

Step-by-step solution

aligned & a ₂₁=-1, a ₂₂=1, a ₂₃=2 & ~A ₂₁=(-1)²⁺¹ | array ll 2 & 3 2 & 4 array |=(-1)(2)=-2 & ~A ₂₂=(-1)²⁺² | array ll 1 & 3 1 & 4 array |=1(1)=1 & ~A ₂₃=(-1)²⁺³ | array ll 1 & 2 1 & 2 array |=(-1)(0)=0 & a ₂₁ ~A ₂₁+ a ₂₂ ~A ₂₂+ a ₂₃ ~A ₂₃=(-1)(-2)+1(1)+2(0) &=3 aligned